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Problem 491

AMC 12 late, AIME early

Number theory Difficulty 4.9 Find the answer

10. Given positive integers $x_{1}, x_{2}, x_{3}, \cdots, x_{2020}$ satisfy $x_{1}+x_{2}+x_{3}+\cdots+x_{2020}=x_{1} x_{2} x_{3} \cdots x_{2020}$ . Then among these 2020 positive integers, the maximum number of values that can be 1 is $\qquad$ .

Your answer

Official solution

$2018$

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.